Bijuus are essentially nothing else but great masses of chakra. If they are still in their host and the host gets killed then the bijuu dies too.
However it doesn't really die in the sense that it is forever gone like the host. After an undetermined amount of time the bijuu appears again on earth free, a danger to everyone and everything it crosses.
That's why they always have a next host nearby when the jinchuuriki dies so that they can seal the bijuu in the next person, without risking it running around freely and upsetting the balance of the villages (a village without a jinchuuriki is in danger of other villages with a jinchuuriki).
I suggest you read the first part however. This way the story will be clearer.